1.
记\(f′(x)\),\(g′(x)\)分别为函数\(f(x)\),\(g(x)\)的导函数\(.\)若存在\(x_{0}∈R\),满足\(f(x_{0})=g(x_{0})\)且\(f′(x_{0})=g′(x_{0})\),则称\(x_{0}\)为函数\(f(x)\)与\(g(x)\)的一个“\(S\)点”.
\((1)\)证明:函数\(f(x)=x\)与\(g(x)=x^{2}+2x-2\)不存在“\(S\)点”;
\((2)\)若函数\(f(x)=ax^{2}-1\)与\(g(x)=\ln x\)存在“\(S\)点”,求实数\(a\)的值;
\((3)\)已知函数\(f(x)=-x^{2}+a\),\(g(x)= \dfrac {be^{x}}{x}.\)对任意\(a > 0\),判断是否存在\(b > 0\),使函数\(f(x)\)与\(g(x)\)在区间\((0,+∞)\)内存在“\(S\)点”,并说明理由.